Non-isothermal Gas Flow Research Articles

A hybrid Gaussian mixture/DSMC approach to study the Fourier thermal problem

In rarefied gas dynamics scattering kernels deserve special attention since they contain all the essential information about the effects of physical and chemical properties of the gas–solid surface interface on the gas scattering process. However, to study the impact of the gas–surface interactions on the large-scale behavior of fluid flows, these scattering kernels need to be integrated in larger-scale models like Direct Simulation Monte Carlo (DSMC). In this work, the Gaussian mixture (GM) model, an unsupervised machine learning approach, is utilized to establish a scattering kernel for monoatomic (Ar) and diatomic (H2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {H}_{2}$$\\end{document}) gases directly from Molecular Dynamics (MD) simulations data. The GM scattering kernel is coupled to a pure DSMC solver to study isothermal and non-isothermal rarefied gas flows in a system with two parallel walls. To fully examine the coupling mechanism between the GM scattering kernel and the DSMC approach, a one-to-one correspondence between MD and DSMC particles is considered here. Benchmarked by MD results, the performance of the GM-DSMC is assessed against the Cercignani–Lampis–Lord (CLL) kernel incorporated into DSMC simulation (CLL-DSMC). The comparison of various physical and stochastic parameters shows the better performance of the GM-DSMC approach. Especially for the diatomic system, the GM-DSMC outperforms the CLL-DSMC approach. The fundamental superiority of the GM-DSMC approach confirms its potential as a multi-scale simulation approach for accurately measuring flow field properties in systems with highly nonequilibrium conditions.

Nonisothermal optimal power and gas flow considering energy storage

The isothermal assumption that treats the gas temperature as a constant is widely adopted in the traditional research. However, the gas temperature has a noticeable effect on the optimal power and gas flow (OPGF) calculation. Moreover, the rational allocation of energy storage can enhance the flexibility and economy of the power and gas system. This paper presents a nonisothermal OPGF considering energy storage, which effectively avoids the constant assumptions on the gas temperature. A simplified partial differential equation which only has bilinear constraints is introduced to depict the temperature change of natural gas. Then, the partial differential equation is discretized by the finite difference scheme and an algebraic pipeline thermal model is developed to avoid the mathematical complexity of the energy conservation equation. The energy storage model is embedded into the OPGF model to enhance the system economy and flexibility. Coupling the DC power flow model and the nonisothermal gas flow model, the nonisothermal OPGF model considering energy storage is formulated. Comprehensive simulations illustrates that the proposed nonisothermal OPGF model considering energy storage can better evaluate the operation state of the integrated energy system. In addition, the energy storage can improve the operation flexibility of systems, thereby significantly reducing the operation costs of the integrated energy systems.

Influence of transport coefficients’ dependence on temperature for gas flow in microbearing

The paper presents an analytical solution for the non-isothermal compressible gas flow in a slide microbearing with different temperatures of walls. The gas flow is defined by the Navier-Stokes-Fourier system of the continuum equations and first order boundary conditions. Knudsen number corresponds to the slip and continuum flow (Kn ≤ 10−1) and Reynolds number is moderately high, so inertia needs to be included. The solution is obtained by perturbations with the first approximation that relates to the continuum flow and the second one that involves second-order effects: the rarefaction, inertia, convection, dissipation, and rate at which work is done in compressing the element of fluid. The presented model analyzes the influence of the dependence of transport coefficients on temperature. The obtained analytical solution for the pressure, velocity, and temperature is approved by a comparison with the results of other authors. The microbearings can often be a part of MEMS, so the presented method and the obtained analytical solution can serve for solving similar non-isothermal shear-driven or pressure-driven problems. The paper gives an estimation about the error in values for microbearing mass flow and load capacity if the dependence of transport coefficients on temperature are neglected.

Influence of wall friction on flow parameters in natural gas transmission pipeline

A mathematical model and computational algorithm are derived for the prediction of natural gas pipeline flow. Non-isothermal and compressible steady-state flow is considered. Heat transfer between gas flow and surroundings is taken into account together with the heat generation due to the gas friction on the inner pipeline wall. The computational algorithm is based on the marching procedure with defined initial conditions. The predicted thermal effect of the wall friction is validated by the simulation of a case that is available in the open literature. The influence of heat generation by gas wall friction in the long transmission pipeline on gas pressure and temperature is evaluated. Differences between results obtained with and without the heat generation due to gas wall friction are analysed. The heat generation due to gas friction on the pipeline inner wall has an influence on the gas temperature change along the pipeline, while its influence on the pressure drop is negligible. These detailed results are novel since most of the previously published results on non-isothermal gas flow did not take into account the thermal effect of the gas wall friction or the influence of this effect was not evaluated. The presented results are a support to the gas pipeline design methods and operational analyses.

Mathematical modeling of non-stationary gas flow modes along a linear section of a gas transmission system

Article demonstrates the applicability of modeling non-stationary non-isothermal gas flow along a linear section of a gas transmission system by means of using various numerically simulated models and sophisticated numerical techniques. There are described several models of non-stationary non-isothermal regimes of gas flow along the pipeline section. They are included in the considered general model and their comparative analysis is carried out by the virtue of numerical simulation. The finite difference algorithm is used to solve the simultaneous equations of the numerically simulated model for the pipeline section. The results of calculating the gas flow parameters using various models are presented: both with and without taking into account kinetic energy, as well as both with and without taking into account the Joule–Thompson effect. The matter of choosing the appropriate model is discussed. The obtained results can be used at the stage of transfer pipeline system operation in order to develop scientifically well-founded recommendations for improving the safety and efficiency of the pipeline transportation system.

Non-Isothermal Optimal Power and Gas Flow

Isothermal natural gas flow model with constant gas temperature has been widely used in conventional coordinated operations of integrated electricity and natural gas systems (IEGS). However, as a crucial state variable in IEGS, gas temperature varies significantly among nodes in a natural gas system, which can be calculated along with nodal pressures and mass flow rates. This paper proposes a novel non-isothermal optimal power and gas flow (OPGF) model that avoids the isothermal assumptions involved in traditional natural gas network model and improves the accuracy significantly. In the proposed model, partial differential terms with minimal weights are neglected based on the quantitative analysis of the energy conservation equation to further simplify the energy conservation equation. A non-isothermal model of natural gas networks is developed by introducing the finite difference method and laws of thermodynamics to incorporate the gas temperature change into the coordinated operation of IEGS. A start point initialization scheme is developed based on the Newton-Raphson algorithm to accelerate the interior point method solution convergence and improve its solution quality. Numerical experiments presented for two test systems validate the effectiveness of the proposed OPGF model and solution methodology.

Determining reservoir parameters with nonisothermal real gas flow

Creation and developing methods of determining gas reservoir properties are one of the most important gas hydrodynamics tasks as production project efficiency and reservoir exploitation depend upon layer properties knowledge. Nonstationary gas hydrodynamics investigations are one of the base well and layer researching methods. Results of these investigations are interpreted based on solving of linear isothermal gas flow equation. The current investigation describes the nonstationary gas hydrodynamic survey results interpretation algorithm, which is based on nonlinear equations system solving. The system consists of nonlinear nonisothermal real gas flow and energy equations accounting well influence, Joule-Thompson and adiabatic expansion effects. Integro-interpolation and iteration finite methods were used for creating their own numerical algorithm. Numerical programs allow solving as direct as inverse gas flow tasks in the cylindrical layer. For verification of inverse task solution, the survey interpretation results from the real gas field were paralleled with currently methods results and showed sufficient accuracy. The described method allows to interpret survey gas hydrodynamic results accounting real gas and porous matrix properties, and well influence to enhance integrity and precision reservoir properties estimation.

Non-isothermal rarefied gas flow in microtube with constant wall temperature

In this paper, pressure-driven gas flow through a microtube with constant wall temperature is considered. The ratio of the molecular mean free path and the diameter of the microtube cannot be negligible. Therefore, the gas rarefaction is taken into account. A solution is obtained for subsonic as well as slip and continuum gas flow. Velocity, pressure, and temperature fields are analytically attained by macroscopic approach, using continuity, Navier-Stokes, and energy equations, with the first order boundary conditions for velocity and temperature. Characteristic variables are expressed in the form of perturbation series. The first approximation stands for solution to the continuum flow. The second one reveals the effects of gas rarefaction, inertia, and dissipation. Solutions for compressible and incompressible gas flow are presented and compared with the available results from the literature. A good matching has been achieved. This enables using proposed method for solving other microtube gas flows, which are common in various fields of engineering, biomedicine, pharmacy, etc. The main contribution of this paper is the integral treatment of several important effects such as rarefaction, compressibility, temperature field variability, inertia, and viscous dissipation in the presented solutions. Since the solutions are analytical, they are useful and easily applicable.

Mathematical Model and Method for Solving the Problem of Non-Isothermal Gas and Liquid Filtration Flow During Dissociation of Gas Hydrates

Mathematical Model and Method for Solving the Problem of Non-Isothermal Gas and Liquid Filtration Flow During Dissociation of Gas Hydrates

Numerical simulation of non-isothermal drainage flow of a viscous gas from a narrow channel

Drainage of a compressed viscous gas from a semi-sealed narrow conduit to a large container is a model problem of fundamental interest to fluid production from subsurface porous rocks. The low Mach number drainage flow exhibits behaviors contrary to predictions from conventional incompressible flow approximations. This work employs direct numerical simulation to study non-isothermal drainage flow from a semi-sealed narrow channel to a laterally bounded large container. The Navier–Stokes characteristic boundary conditions are implemented at the open boundary downstream in the computational domain to avoid spurious wave reflection. For a laterally bounded container, wave transport dominates the drainage process. It is shown that in the absence of an imposed temperature drop, thermal effect slows down the drainage process with adiabatic walls. With large enough temperature drop, thermal effect speeds up the drainage, and it also produces excess mass beyond that of the isothermal model. These thermal effects are consistent with the previous results for a laterally unbounded container in a linear theory.

The effect of Stefan flow on Nusselt number and drag coefficient of spherical particles in non-isothermal gas flow

A Stefan flow can be generated during a phase change or reactions of a particle immersed in a fluid. This study investigates the effect of Stefan flow on the exchange of momentum (drag coefficient (CD)) and heat transfer (Nusselt number (Nu)) between the particle and bulk-fluid. Fully resolved simulations were carried out for a flow near a spherical particle immersed in a uniform bulk flow. The immersed boundary method is used for implementing fluid-solid interactions and the particle is considered as a static boundary with fixed boundary conditions. In a non-isothermal flow, the changes in thermophysical properties at the boundary layer played a role in the variation of CD and Nu by a Stefan flow further. The previously developed model for the drag coefficient of a spherical particle in a uniform isothermal flow was modified for a uniform non-isothermal flow. The model is developed based on physical interpretation. A new model is developed for the Nusselt number for a spherical particle with a uniform Stefan flow combining available models in literature. The models are validated for Stefan Reynolds number −8⩽Resf,p⩽25 and particle Reynolds number of 2⩽Ref⩽30 in gas flow (i.e. Pr≈0.7).

Numerical analysis of dual porosity coupled thermo-hydro-mechanical behaviour during CO2 sequestration in coal

This study presents a coupled dual porosity thermal-hydraulic-mechanical (THM) model of non-isothermal gas flow during CO2 sequestration in coal seams. Thermal behaviour is part of the disturbed physical and chemical condition of a coal seam caused by CO2 injection, and must be understood for accurate prediction of CO2 flow and storage. A new porosity-permeability model is included for consideration of the fracture-matrix compartment interaction. The new model is verified against an analytical solution and validated against experimental measurements, before being used to analyse coupled THM effects during CO2 sequestration in coal. A simulation of CO2 injection at a fixed rate shows the development of a cooling region within the coal seam due to the Joule-Thomson effect, with the temperature in the vicinity of the well declining sharply before recovering slowly. The temperature disturbance further from the well is more gradual by comparison. Under the simulation conditions studied, CO2 injection increases coal matrix porosity and decreases the porosity and permeability of the natural fracture network, especially in the vicinity of the injection well, due to adsorption-induced coal swelling. Compared with the effects of gas pressure and temperature, the matrix-fracture compartment interaction plays an important role in changes of porosity and permeability. Considering the temperature disturbance caused by CO2 injection under the set of representative conditions studied, the coupled model can provide an insight into the associated effects on CO2 flow and storage during its sequestration in coal seams.

Modified lattice Boltzmann solution for non-isothermal rarefied gas flow through microchannel utilizing BSR and second-order implicit schemes

Thermal microscale gas flow was simulated into a coplanar microchannel was simulated at a broad range of Knudsen numbers. Attempts were made to improve the accuracy of slip velocity on walls using a modified model with two relaxation times based upon the mesoscopic method. The temperature jump of fluid flow at the wall was captured by a model with a single relaxation time using a second-order implicit method. The Zou–He boundary conditions were employed at both inlet and outlet boundaries, and bounce-back/specular reflection distribution functions were applied to the impermeable walls. The non-equilibrium distribution functions were also used as the inlet temperature boundary condition. A fully developed temperature profile was considered at the microchannel outlet. A pressure ratio of 2 was considered in the simulations, and various parameters such as dimensionless pressure, pressure deviation from the linear pressure, dimensionless velocity at various Knudsen numbers, centerline velocity and slip velocity of the fluid, centerline temperature and fluid temperature on the wall, Nusselt number with changing Knudsen and Prandtl numbers, parameter k along the microchannel length and Cf·Re values were evaluated in the slip and transition flow regimes. The results of the direct simulation Monte Carlo were used to evaluate the correctness of the numerical model. The consistency of the two methods indicated the accuracy of the proposed method.

Nonisothermal Rarefied Gas Flow through a Long Cylindrical Channel under Arbitrary Pressure and Temperature Drops

The problem of rarefied gas flow through a long cylindrical channel as a function of the pressure and the temperature maintained at the channel ends is considered on the basis of the S-model of the Boltzmann kinetic equation. The pressure and temperature drops between the channel ends vary from small values at which the linear transport theory is valid to large values at which the gas molecule mean free path ceases to be constant along the channel. The solution to the model kinetic equation is found by means of the collocation method using the Chebyshev polynomials and rational functions. The mass flow and the pressure in the channel are obtained. Isobaric and isothermal flows are investigated.

Underground Storage of Natural Gas in Hydrate State: Numerical Experiment

The paper is devoted to simulation of the initial stage of natural gas hydrate underground storage: gas injection into aquifer just below permafrost rocks. It is based on the mathematical model of multiphase non-isothermal real gas and water flow in porous media. The model takes into account the transformation of gas and water into hydrate at certain temperature which depends on gas flow pressure. The dynamics of hydrate and water saturation as well as the pressure and temperature fields in a reservoir with given porosity, permeability and initial values of pressure, temperature and water saturation have been studied. An implicit finite-difference scheme is used to approximate the original boundary-value problem. The finite-difference equations have been solved using simple iteration and sweeping algorithms. Several examples of calculations corresponding to real cases are given. Calculations have revealed that the final result strongly depends on the combination of porosity and permeability of a reservoir.

Impact of Thermal Models on the Performance of Natural Gas Pipelines

AbstractThis study investigates the energy savings in the nonisothermal flow of natural gas during its pipeline transportation compared to the isothermal flow. Isothermal and nonisothermal models a...

A Smooth Dissipative Particle Dynamics method for nonisothermal liquid and gas flows in bounded domains

A Smoothed Dissipative Particle Dynamics formulation with dynamic virtual particle allocation (SDPD-DV) is developed for the simulation of mesoscale nonisothermal flows with non-slip, constant temperature and constant heat flux boundary conditions. For liquids, the particle internal energy is evaluated through a first-order expansion from an initial volume and entropy state. For liquids, the particle pressure and temperature are evaluated using the coefficients of adiabatic compressibility, volumetric thermal expansion and heat capacity. For monatomic and diatomic gases, the fluid particle internal energy is evaluated through a Sackur-Tetrode type of equation. For both liquids and gases, the viscosity and thermal conductivity are modeled by a power law. Integration of position and momentum equations is performed with a velocity-Verlet method and bounce-forward reflection. Integration of the entropy equation is performed with a Runge-Kutta method. Verification of SDPD-DV is performed for planar isothermal Couette, planar Fourier, and planar nonisothermal Couette flows of liquid H2O and gaseous N2, and for a nonisothermal planar Poiseuille flow of a fluid with an exponential temperature-depended viscosity. SDPD-DV simulations for liquid H2O, gaseous Ar and N2 systems under thermal equilibrium assess the impact of the ratio of particle mass (mi) over the real molecular mass and the size of smoothing length (h) on fluid properties, hydrodynamic fluctuations and transport coefficients. For liquid systems the density fluctuations exhibit scatter about the analytical estimates and the temperature fluctuations follow the analytical estimates for mass ratios smaller than 10,000. The velocity fluctuations are in excellent agreement with theoretical estimates. For gases, the density fluctuations exhibit scatter about the analytical estimates and the pressure fluctuations agree with the analytical estimates for mass ratios smaller than 10,000. The temperature and velocity fluctuations are in excellent agreement with the analytical estimates. The self-diffusivity evaluated from SDPD-DV simulations for liquid and gases is shown to increase with smoothing length for a given mass ratio, scales with h2/mi and is in excellent agreement with analytical estimates. The shear viscosity evaluated from SDPD-DV simulations for liquid and gases exhibits scatter around the experimental values and is shown to be scale free.

Numerical modeling of compressible gas flow in zeolite bed and above its surface

In contemporary models of adsorption of gases inside porous media, only the porous medium is modeled, although it can be important to predict what happens, e.g., inside a pipe through which the gas comes into the porous medium. Therefore, we choose one of the adsorption phenomena studied in the literature (adsorption of water on zeolite particles) and propose mathematical and numerical models for non-isothermal compositional compressible gas flow in a zeolite bed and in an adjacent boundary layer of atmospheric flow above its surface, where one of the flowing components adsorbs on the zeolite particles. In order to assess the reliability of our numerical model, we analyze its convergence and its sensitivity to changes in numerical parameters.

Transient heat transfer and non-isothermal particle-laden gas flows through porous metal foams of differing structure

Multiphase solid-gas flows and particulate fouling in porous media are omnipresent in many environmental and industrial applications. However, the underlying mechanisms and transport behaviour of these complex fluids coupled with heat transfer effects are poorly understood. Moreover, the complexity of multiphase non-isothermal solid-gas transport is further compounded by the fact that thermal solid-gas transport through porous metal foams is not established. This paper numerically investigates non-isothermal solid-gas flows through an idealized metal foam heat exchanger based on a cylindrical ligament and a Weaire-Phelan model. We delve into the dynamics and heat transfer profiles of solid-gas flows immersed in porous metal foams based on various solid foulant properties. The foulant thermal behaviour based on various metal foam ligament wall temperatures is investigated. It is found that the foulant temperature profiles vary with time and the temperature profiles also vary with increasing wall temperature. Moreover, the Weaire-Phelan (WP) model can be used as an alternative to the real metal foam sample. The heat transfer between the foulant, wall, and fluid play a pivotal role in the alteration of the temperature profiles. The developed numerical methodology and the WP geometry may serve as a stepping-stone to address pertinent issues such as indoor environmental studies and optimization of compact heat exchangers.

Nonisothermal Free-Molecular Flow of Gas in an Elliptic Channel with a Circular Cylindrical Element Inside

The linearized problem of free-molecular gas flow in a long elliptic channel with a circular cylindrical element inside has been solved in the kinetic approximation. The flow in the channel is caused by temperature and pressure drops between its ends. The Boltzmann kinetic equation for collisionless gas has been used as a basic equation, and the boundary condition has been set in terms of the diffuse reflection model. The distribution of the mass velocity of the gas over the cross section of the channel has been obtained. The mass flow rate of the gas in the channel versus the temperature and pressure drops between its ends has been calculated. It has been found that the mass flow of the gas substantially depends on the radius of the inner cylinder.